• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.469-474
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• 2015

In this paper, we will consider the notions of (m, n)-potent conditions in near-rings, in particular, a near-ring R with left bipotent or right bipotent condition. We will derive some properties of near-rings with (1, n) and (n, 1)-potent conditions where n is a positive integer, and then some properties of near-rings with (m, n)-potent conditions. Also, we may discuss the behavior of R-subgroups in (1, n)-potent or (n, 1)-potent near-rings..

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.555-565
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• 2014

An ideal I of a ring R is strongly ${\pi}$-regular if for any $x{\in}I$ there exist $n{\in}\mathbb{N}$ and $y{\in}I$ such that $x^n=x^{n+1}y$. We prove that every strongly ${\pi}$-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any $x{\in}I$ there exist two distinct m, $n{\in}\mathbb{N}$ such that $x^m=x^n$. Furthermore, we prove that an ideal I of a ring R is periodic if and only if I is strongly ${\pi}$-regular and for any $u{\in}U(I)$, $u^{-1}{\in}\mathbb{Z}[u]$.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.407-421
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• 2004

By using a recursive algorithm, we construct edge-coloured graphs representing products of spheres and consequently we give upper bounds for the regular genus of ${\mathbb{S}}^{m}\;\times\;{\mathbb{S}}^{n}$, for each m, n > 0.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.373-385
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• 2009

An m${\times}$n Boolean matrix A is called regular if there exists an n${\times}$m Boolean matrix X such that AXA = A. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.21-30
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• 2021

In this paper, we prove some rigidity results about embedded minimal hypersurface M ⊂ ℝn+1 with compact ∂M that has one end which is regular at infinity. We first show that if M ⊂ ℝn+1 meets a hyperplane in a constant angle ≥ ��/2, then M is part of an n-dimensional catenoid. We show that if M meets a sphere in a constant angle and ∂M lies in a hemisphere determined by the hyperplane through the center of the sphere and perpendicular to the limit normal vector nM of the end, then M is part of either a hyperplane or an n-dimensional catenoid. We also show that if M is tangent to a C2 convex hypersurface S, which is symmetric about a hyperplane P and nM is parallel to P, then M is also symmetric about P. In special, if S is rotationally symmetric about the xn+1-axis and nM = en+1, then M is also rotationally symmetric about the xn+1-axis.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.389-394
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• 1999

A v-path of an arc xy in a multipartite tournament T is an oriented oath in T-y which starts at x such that y does not dominate and end vertex of the path. We show that if T is a regular n-partite (n$\geq$7) tournament, then every arc of T has a v-path of length m for all m satisfying 2$\leq$m$\leq$n-2. Our result extends the corresponding result for regular tournaments, due to Alspach, Reid and Roselle [2] in 1974, to regular multipartite tournaments.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.373-384
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• 2011

In this paper we introduce and give some characterizations of (m, n)-regular le-${\Gamma}$-semigroup in terms of (m, n)-ideal elements and (m, n)-quasi-ideal elements. Also, we give some characterizations of subidempotent (m, n)-ideal elements in terms of $r_{\alpha}$- and $l_{\alpha}$- closed elements.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.15-20
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• 2001

Reduced Von Neumann Regular ring is pseudo symmetric and N(R) is reduced. Thus N(R) is pseudo symmetric and M(R) is reduced if and only if M(R) = N(R).

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.261-266
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• 2003

In this paper, we described the structure of coextensions of regular semigroups by rectangular bands.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1333-1338
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• 2018

A ${\ast}-ring$ R is called ${\ast}-regular$ if every principal one-sided ideal of R is generated by a projection. In this note, several characterizations of ${\ast}-regular$ rings are provided. In particular, it is shown that a matrix ring $M_n(R)$ is ${\ast}-regular$ if and only if R is regular and $1+x^*_1x_1+{\cdots}+x^*_{n-1}x_{n-1}$ is a unit for all $x_i$ of R; which answers a question raised in the literature recently.